I'm not sure if this is actually jazz or blues, but the vibe is there.
Cool Out - Zero 7
One of my favorites are The Seatbelts, they done a lot of music for an anime called Cowboy Bebop, they have a very diverse style, some of their stuff is really good.
The Farewell Blues - The Seatbelts
Honestly I don't know that many artists, was hoping someone could show me some stuff.
Smoke durries, eat curries.